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The Western Mesopotamian Derived Time System In Contrast To The Precolonial Hindu (Vedic)

Time System Brought Together As Natural By A Physics Theory For Aspects Of Reality And

Ancient Aliens Are Suggested!

By!

Ian Beardsley!

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Important To Point Out

You can speak of the structure of the solar system even though it changes with time. This is

important to understand when I refer to sizes of the Moon and the planets, and their orbital

distances.

The whole object of developing a theory for the way planetary systems form is that they meet the

following criterion: They predict the Titius-Bode rule for the distribution of the planets; the

distribution gives the planetary orbital periods from Newton’s Universal Law of Gravitation. The

distribution of the planets is chiefly predicted by three factors: The inward forces of gravity from

the parent star, the outward pressure gradient from the stellar production of radiation, and the

outward inertial forces as a cloud collapses into a flat disc around the central star. These forces

separate the flat disc into rings, agglomerations of material, each ring from which a different

planet forms at its central distance from the star (it has a thickness). In a theory of planetary

formation from a primordial disc, it should predict the Titius-Bode rule for the distribution of

planets today, which was the distribution of the rings from which the planets formed.

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Contents

Abstract………………………………………………………………………….4

Introduction……………………………………………………………………..5

The Ancient Vedic System Of Measuring Time…………………………..6

A Theory For Reality With A Base Unit Of A Second…………………….7

Conclusion…………………………………………………………………………15

Ancient Aliens……………………………………………………………………17

Biological Life Part of a Universal

Natural Process In The Universe………………………………………….34

The Solar Formulation For The Solution Of

The Wave Equation…………………………………………………………….41

Wave Solutions For Jupiter And Saturn……………………………….50

Modeling Habitable Star Systems…………………………………………55

Appendix 1…………………………………………………………………………61

Appendix 2: The Data For Verifying The Equations…………………….63

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Abstract

I have a theory for reality that solves the proton of atoms and the solar system as a habitable

planetary system and the basic structure of biological chemistry. It is based on the unit of a

second as the base unit and as a natural constant. This is peculiar because the second comes

to us from the Ancient Sumerians of Mesopotamia who could not have known of modern

physics and astronomy. However, I now look at the precolonial Hindu Vedic system for

measuring time and ﬁnd it is just as intriguing, and my theory has equations that bridge the

two. They could not have known about modern physics either. I take a look at ancient aliens,

and ﬁnd perhaps a trace of their presence in the development of our astronomy since ancient

times. There is an eﬀort in India to return to the old system before the British Colonization, and

they suggest their ancient system might be more well suited to modern science, however my

physical theory of reality suggests both systems are important and that both are founded on

Nature."

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Introduction

I came up with a physical theory for certain aspects of reality that showed that our solar system

had a wave equation solution, where the wave equation was developed for describing atomic

systems, among other things, and is at the heart of quantum physics, the modern physics that

describes thing on the micro-scale and our planetary system is on the macro-scale. I found it

was based on the Moon that orbits the Earth, which seems to be some kind of a natural

yardstick, and was further based on the unit of a second for measuring time as the base unit,

which I found turns out to be some kind of a natural constant. This natural constant of a

second also, in the theory, predicts the radius of a proton, the fundamental unit of the atom,

and as such a gap is bridged between the microcosmos and the macrocosmos. Further it

resulted in a description of the hydrocarbons, which are the backbones of the chemistry of life.

Bringing in the biological like this makes it the rudiments of a theory of everything,!

The interesting thing is, though, that the second was not designed, originally, as a natural

constant, but came to us ultimately from the ancient Sumerians of Mesopotamia, who were

some of the ﬁrst to settle down from hunting with stone spearpoints to invent agriculture,

mathematics, writing, metallurgy, architecture… to invent civilization.!

The idea was to divide the day into twelve hours, and measure each hour by the position of the

Sun in the sky, as measured by the shadow cast by a rod onto a plate with lines to measure the

time of day. They chose twelve hours in a day because 12 is the smallest abundant number,

which is to say it is evenly divisible by 1,2,3,4,6 whose sum is 16 which is greater than twelve. !

Their counting system was base 60 (sexagesimal) which means they started counting again

after counting to 60 where our system is base 10 (decimal) which mean we start counting again

after 10. They chose base 60 because sixty, aside from being an abundant number — its

divisors add up to a value greater than it, it is the ﬁrst number divisible by the ﬁrst 6 counting

numbers, 1,2,3,4,5,6 aside from being evenly divisible by 10,12,15,30.!

This lead to the ancient Babylonians dividing the hour into 60 minutes, and the minute into 60

seconds. This in the end lead to the ancient Greeks using it for astronomy, and the Italians to in

the Middle Ages build the ﬁrst clocks with hours, minutes, and, seconds. In the end they gave

us our clocks and they way we measure time in the West, today. The ancient Egyptians,

separately and independently invented civilization from the Sumerians, but were never invaded

by tribes, like in Sumer, who stayed and adopted their math and writing, but rather were

isolated by desert, ocean, and forests, so as not to spread their invention of Mathematics,

writing, and architecture to the rest of the world, at least until they and the ancient Greeks

interacted and shared knowledges in several exchanges where ancient Greek scholars

wandered into Egypt. But, the ancient Egyptians also divided the day into 12 hours and

invented sun dials to tell time as such. However, we got the 12 hour day, or 24 hour day from

sunrise to sunrise and sunset to sunset, from the ancient Sumerians.!

However, myself, having been born in the West I was more aware of Sumer and Egypt, than

India, and indeed while Sumer and Egypt started civilizations, so did the people who brought it

to India, to the Dravidians, and the idea of transmigration of the soul who were from its

outskirts, who brought it from the Indus Valley where the rivers were, they were the Indus Valley

Civilization, just as old as Sumer and Egypt. It would seem civilizations always started along

rivers, the Tigris and Euphrates in Mesopotamia, and the Nile in Egypt.!

However, after having looked at my theory for reality in terms of the base 60 of Sumer that gave

us the second, and how its dynamics could have coincided with modern physics, and

suggesting that it was given to them by ancient Aliens, because they said they got their

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knowledge from those who came from the heavens, the Anunaki, I began to look at the system

that ancient India used to measure time, and I found that they used base 60 as well, but in a

very reversed way from what we got from Mesopotamia, the Babylonians, and ancient Greeks.

And, I found further, that their system of base 60 describes certain aspect of Nature as well.!

The Ancient Vedic System Of Measuring Time

Before the colonization of India by the British, another system of measuring time from ancient

times was used, and it was called the Bharat Clock. There are eﬀorts in India today to return to

this, and they suggest for contemporary physics it serves better, as well as it is more eﬃcient

for productivity in the work force. Further still they explain that it is based on Natural

Phenomenon in the Universe, and that in the method of the West, it is not. I would take issue

with that not just because my theory for reality shows the Mesopotamian system gives us the

unit of a second in planetary systems, atomic systems, and biological systems, which they

could not know about, but because it does have an elegance that works well for the the

periods of celestial motions, and has since its inception, though I can see advantages in their

system as well.!

The Hindu system is quite inverted from ours, but my theory of physical reality shows the two

systems are profoundly connected in a way that can be quite revealing. We measure the year

as 365.25 days which is close to the 360 degrees in a circle. As such the Earth moves around

the Sun in its orbit through neatly about 1 degree per day. The Sumerians gave us the 360

degrees circle, because in their base 60 counting 6 times 60 is 360, and 6 is the most dynamic

number, a six-sided regular polygon has its radii equal to its sides, which mathematically has

many advantages for solving problems. It occurs in Nature as the closest packing of equal

radius spheres, the so so called six around one, typical in Nature of petal arrangements around

a center in a ﬂower, and 6-fold symmetry is typical of the physical, like snowﬂakes forming six-

points as ice crystals fall through cold air. 5-fold symmetry is typical of life, like two eyes and

nose and a mouth, or two arms, two legs, and a head.!

The Earth then rotates close to 360 times in a year, close to the time for it to complete an orbit

around the Sun. Each rotation is a day, and from the Sumerians we divided that day into 24

hours. 60 divided by 24 is 2.5 and as it would turn out 2.5 is the factor than connects the Hindu

system to the Western system. As we shall see, my theory ﬁnds this factor in a pivotal factor of

Nature. Let’s look at our system and theirs. We have!

(365.25 days)(24 hours)(60 minutes)(60 seconds)=31557600 seconds/year!

And the seconds in a day are!

(24 hours)(60 minutes)(60 seconds)=86400 seconds/day!

Thus we divide the hour into 60 minutes, and the minutes into 60 seconds. The Hindu Vedic

System has a day is 60 ghatika of 24 minutes each, each ghatika is divided into 60 palas of 24

seconds each, and each pala is divided into 60 vispalas, each vispala of 0.4 seconds each. So

where our system has a base unit of 1 second, theirs has a base unit of 0.4 seconds, so that

could be and advantage to their system, a smaller unit of time is more reﬁned. Further their day

is divided into 60 units, ours into only 24, so their hour, the ghatika is only 24 minutes long, and

ours is 60 minutes long, The proponents in India say since when working and doing chores we

do a few chores in an hour, they do about one per ghatika is 24 minutes, which makes the

measure of time more manageable. That could be an advantage I think. They say our hour is so

long because the lines had to be far apart on the Egyptian Sun Dial so the shadow cast by the

Sun didn’t cross-over onto another line. But today, with modern technology we can make clock

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lines marking hours closer together and measure them with a pointer hand pointing to them

without any problems, and the result is we have would have a smaller more reﬁned hour (60 of

them in a day as opposed to 24). They suggest this method of measuring time would work

better in science and engineering as well, that we have to get away from the way sun dials had

to be made in Egypt in ancient times.!

But they further point out that their system describes Nature. They say theirs are 108,000

vispalas in a day, and 108,000 vispalas in a night giving 216,000 vispalas in a 24 hour day. The

diameter of the Sun is 108 that of the Earth, and the average distance from the Sun to the

Earth is 108 solar diameters, and the average distance from the Moon to Earth is 108 lunar

diameters. 108(10)(10)(10)=108,000. Ourselves and them use base 10 counting, and that is

probably because we have ten ﬁngers to count on.!

A Theory For Reality With A Base Unit Of A Second

So it is at this point that I would like to go into my theory of reality that shows the second is a

base unit and a natural constant as well. In the Bharat Clock they don’t use the second, their

base unit is 0.4 seconds.!

The second I found is the base unit of the orbital dynamics of the solar system. I found I could

create three operators, one that acts on the radius of the proton to its mass, and the other that

acts on the radius of the Sun to its mass, and one that acts on angular momentum to speed.

is Planck’s constant, is the universal constant of gravitation, is the speed of light, is the

ﬁne structure constant, is the radius of a proton, is the mass of a proton, is the mass

of the Moon, is its radius, and the EarthDay is the rotation period of the Earth:!

They seem to suggest that the Earth orbit might by quantized in terms of the Moon and a base

unit of one second.

We say there is a Planck constant for the solar system. We do it with a base unit of one second

because equations 1 and 2 suggest we should . We suggest it is such that it is given by the

standard Planck constant for the atom, , times some constant, , and the Kinetic energy of the

Earth.

(

6α

4πh

)

⋅

= 1secon d

(

(Ear th Da y)

)

⋅

⊙

= 1secon d

⋅

π r

G m

⋅

= 1secon d

ℏ

⊙

= (hC )K E

hC = 1secon d

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Where

6).

Where equation 6 comes from equation 3.

We derive the value of our solar Planck constant

Now we show that our Planck constant for the solar system gives the base unit of one second for

the quantization. We call our solar Planck constant and find the wavelength for the Moon

which is the ground state for the solar system:

C =

⋅

π r

G m

C =

⋅

2π r

G m

⋅

18769

299792458

⋅

2π (0.833E − 15)

(6.67408E − 11)(1.67262E − 27)

1.55976565E 33

⋅

kg ⋅ m

⋅

= kg

= energ y

hC = (6.62607E − 34)(1.55976565E33) = 1.03351secon ds ≈ 1.0secon ds

hC =

(

⋅ m ⋅ s

)

(

⋅

)

(

)(

⋅

)

= secon d s

K E

earth

(5.972E 24kg)(30,290m /s)

= 2.7396E 33J

ℏ

⊙

= (hC )K E

earth

= (1.03351s)(2.7396E 33J ) = 2.8314E 33J ⋅ s

ℏ

⊙

moon

ℏ

⊙

(2.8314E 33)

(6.67408E − 11)(7.34763E 22kg)

= 3.0281E8m

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Then wavelength associated with the Moon divided by the speed of light should be 1 second if

our planetary system is quantized in terms of the Moon and a base unit of one second. We have

And we see it is, so we have

The solution for the orbit of the Earth around Sun with the Schrödinger wave equation can be

inferred from the solution for an electron around a proton in the a hydrogen atom with the

Schrödinger wave equation. The Schrödinger wave equation is, in spherical coordinates

10)

Its solution for the atom is

11)

12)

is the energy for an electron orbiting protons and , is the orbital shell for an electron with

protons, the orbital number. I find the solution for the Earth around the Sun utilizes the

Moon around the Earth. This is different than with the atom because planets and moons are not

all the same size and mass like electrons and protons are, and they don’t jump from orbit to

orbit like electrons do. I find that for the Earth around the Sun

13)

14)

is the kinetic energy of the Earth, and is the planet’s orbit. is the radius of the Sun,

is the radius of the Moon’s orbit, is the mass of the Earth, is the mass of the Moon, is

the orbit number of the Earth which is 3 and is the Planck constant for the solar system.

Instead of having protons, we have the radius of the Sun normalized by the radius of

the Moon. It is has always been an amazing fact the the sizes of the Moon and the Sun are such

that given their orbital distances, the Moon as seen from the Earth perfectly eclipses the Sun.

This becomes part of the theory and we suggest it is a condition for sophisticated planets that

harbor life by writing it:

moon

3.0281E8m

299,792,458m /s

= 1.010secon d s

moon

= 1secon d

−

ℏ

[

∂

∂r

(

∂

∂r

)

sinθ

∂

∂θ

(

sinθ

∂

∂θ

)

sin

∂

∂ϕ

]

ψ + V(r)ψ = E ψ

E = −

)

2ℏ

ℏ

Z k

K E

= n

⊙

⋅

2ℏ

⊙

2ℏ

⊙

⋅

⊙

⋅

K E

⊙

ℏ

⊙

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15)

That is the orbital radius of the planet (Earth) to the orbital radius of its moon (The Moon) is

about equal to the the radius of the star (The Sun) to the radius of its moon (The Moon). We say

the system is quantized by the Moon and the base unit of one second. It is a fact that the Moon

orbiting the Earth optimizes the conditions for life on Earth because it holds the Earth at its

inclination to its orbit around the Sun allowing for the seasons, preventing extreme hot and

extreme cold. Let us now see if our solar Planck constant works…

16)

=2.727E36J

The kinetic energy of the Earth is

The accuracy of our equation is:

Which is very good. Thus we have solved the Earth/Moon/Sun System with our spacetime

operators by using them to find a Planck constant for the solar system.

We want to suggest that the base 60 dynamic applied to the rotational velocity of the Earth to

measure time has a natural property associated with the atom and the Earth/Moon/Sun orbital

system as a solution to the atom’s wave equation. The Earth day is given by, in seconds

This gives since

Thus we have as factors for the seconds per day the smallest primes 2 and 3, and the 4 of

rectangular coordinate systems, and the versatile, abundant, 60. We then suggest the second is

dynamic in terms of what the ancients gave us because 86400 seconds comes from

and this I suggest is connected to Nature because the Earth rotates at a speed

that gives from these ancient factors the duration of a second that I found is the base unit of the

atomic systems and our planetary system, in particular of our Earth/Moon/Sun system as a

solution of the Schrödinger wave equation that solves the same atomic system, which I will go

into right now.

planet

moon

≈

star

moon

⊙

6.96E8m

1737400m

= 400.5986

K E

= (1.732)(400.5986)

(6.67408E − 11)

(5.972E 24kg)

(7.347673E 22kg)

2(2.8314E 33)

K E

(5.972E 24kg)(30,290m /s)

= 2.7396E 33J

2.727E 36J

2.7396E 33J

100 = 99.5 %

(

1d a y

24hrs

)(

1hr

60mi n

)(

1min

60sec

)

86400

d a y

sec

2 ⋅ 3 ⋅ 4 = 24

2 ⋅ 3 ⋅ 4 ⋅ 60 ⋅ 60 = 86400secon d s /d ay

2 ⋅ 3 ⋅ 4 ⋅ 60 ⋅ 60

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We see the spacetime operators solve the atom by giving us the radius of a proton. We set

equation 3 equal to equation 1

1).

These two yield

17).

I find this is close to the experimental value of the radius of a proton. I find I can arrive at this

radius of a proton another way, energy is given by Planck’s constant and frequency

We have

We take the rest energy of the mass of a proton :

The frequency of a proton is

Since our theory gave us the factor of 2/3 for the radius of a proton we have:

The radius of a proton is then

⋅

π r

G m

⋅

= 1secon d

(

6α

4πh

)

⋅

= 1secon d

⋅

E = h f

f = 1/s, h = J ⋅ s, h f = (J ⋅ s)(1/s) = J

E = J = Joules = en erg y

E = m

⋅

≈ ϕ =

⋅

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This is close to the CODATA value for the proton radius around 2018 (0.842E-15m). The result

We find it may be that the radius of a proton is actually

18)

Where is the golden ratio constant (0.618…). This is more along the lines of more recent

measurements. Both equations 17 and 18 for the radius of the proton can be right depending on

the dynamics of what is going on; the radius of a proton is not precisely defined, it is more of a

fuzzy cloud of subatomic particles. Thus we have solved the atom with our spacetime operators

by producing the radius of a proton.

Indeed if the dynamics of the factors the ancients gave us to create the duration of a second are

connected to the dynamics of star systems then then the second should define the rotational

angular momentum of the Earth since we divide the rotation period of the Earth into these

factors to get the unit of second, and should be connected to our Planck constant for the solar

system which is in units of angular momentum as well, as is Planck’s constant for the atom.

The angular momentum of the Earth with respect to the Sun is 2.66E40 kg m2/s. The rotational

angular momentum is 7.05E33 kg m2/s. In orbit angular momentum is given by

For a uniform rotational sphere it is given by

We found our solar system Planck constant was

This gives

19)

We are now equipped to show that the ancient Sumerians were right in dividing the rotation

period of the Earth (the day) into 24 units (the hour) because

That is

⋅

6.62607E − 34

(299,792,458)(1.67262E − 27)

= 0.88094E − 15m

= ϕ ⋅

= 0.816632E − 15m

L = 2π M f r

L =

π M f r

ℏ

⊙

= 2.8314E 33J ⋅ s

earth

ℏ

⊙

7.05E 33

2.8314E 33

= 2.4899 ≈ 2.5 = 2

2.5(24) = 60

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20).

Which is to say the angular momentum of the Earth to its Planck constant gives the base 60

counting in terms of the 24 hour day, the 60 of 60 minutes in an hour, and 60 seconds in a

minute, that determine our base unit of duration we call a second that happens to be, as I have

shown, the base unit of the wave solution to the atom and the Earth/Moon/Sun system.

Our equation in this paper for the Earth energy as a solution of the wave equation (eq. 13)

13).

does not depend on the Moon’s distance from the Earth, only its mass. The Moon slows the

Earth rotation and this in turn expands the Moon’s orbit, so it is getting larger, the Earth loses

energy to the Moon. The Earth day gets longer by 0.0067 hours per million years, and the

Moon’s orbit gets 3.78 cm larger per year. Equation 20

20)

only specifies divide the day into 24 units, and hours into 60 minutes and minutes into 60

seconds, regardless of what the Earth rotational velocity is. But it was more or less the same as it

is now when the Sumerians started civilization. But it may be that it holds for when the Earth

day is such that when the Moon perfectly eclipses the Sun, which we said might be a condition

for the optimization of life preventing extreme hot and cold. That is when 15 holds

15)

Which holds for today and held for the ancient Sumerians and holds for when the Earth rotation

gives the duration of a second we have today.

We want the basis set of equations for the solar system. We have

We have from equation

We have equations

earth

ℏ

⊙

24 = 60

K E

= n

⊙

⋅

2ℏ

⊙

earth

ℏ

⊙

24 = 60

planet

moon

≈

star

moon

ℏ

⊙

= 3.0281E8m

moon

ℏ

⊙

⋅

= 1.0secon d s

ℏ

⊙

= (hC )K E

hC = 1secon d

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We have equations

(This Equation is how I got Equation 2.)

From these it becomes clear that

21)

22)

23)

Thus combining equation 20 with the following…

21).

20).

gives

Which gives

⋅

π r

G m

⋅

= 1secon d

(

6α

4πh

)

⋅

= 1secon d

1secon d =

K E

(Ear th Da y)

ℏ

⊙

K E

ℏ

⊙

ℏ

⊙

(

6α

⋅

4πh

)

K E

moon

= 1secon d

hC = 1secon d

ℏ

⊙

= (hC )K E

K E

ℏ

⊙

earth

ℏ

⊙

24 = 60

1secon d =

(

)

earth

of 15 65

24)

This is very accurate to give us a second. But notice 6.262 is approximately . We see that

25)

is the circumference of a unit circle, it could be that the circumference of the Earth orbit, can

be taken as 1 (unity) and essentially we have the mystery of base 60 and the 24 hour day of the

ancient Sumerians is solved, it connects unit circle to 1 (unity).

26).

27)

Conclusion

In conclusion we have that the unit of a second as derived from the Mesopotamians is a Natural

constant. As well we see the Hindu Vedic system describes Nature as well. It says

( )

1secon d =

(

)

earth

(

)

(7.05E 33)

(6.67408E − 11)((7.347673E 22kg)

(299792458m /s)

(

)

6.262sec = 1.002secon d s = 1.00secon ds

2π

1 =

(

)

2π

cos(45

∘

) = cos(π /4) =

⊙

= 2(6.957E8m) = 1.3914E 9m eters

⊙

= Sol arRa dius

= 1.496E11m

= Ear thOrbit

⊙

= 107.52 ≈ 108

moon

= 2(1.74E6m) = 3.48E6m

moon

= Lu n arRa diu s

moon

= 3.845E8m

moon

= Lu n ar Orbit

moon

= 110 ≈ 108

(86,000sec /d a y)

43200

0.4sec /vispala

= 108,000vispal a s /d a y

108(10)(10)(10) = 108,000

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To see how this is connected to nature we would have to go into the significance of base 10

counting as we did with base 60 counting. But interesting here is that

because

13.

where

15.

16.

Which is to say radius of the Sun to the radius of the Moon in the planetary equation plays the

role of the number of protons (Z) in an element for the energy of the electron orbits in the

atomic equation and that the Moon perfectly eclipses the Sun as see from the earth (eq 15) might

be a condition for sophisticated habitable star systems, we know the Moon allows for the

seasons making life very successful on Earth by preventing temperature extremes. So in the

Hindu Vedic system the diameters of the Sun and Moon fitting into Earth orbit and Lunar orbit

the same amount might play a similar role in a theory. You would have to go into base 10 like we

did with base 60. We have

West

24 hours

60 minutes

60 seconds

India

60 hours

24 minutes

24 seconds

A sort of inversion of things. The incredible thing here is that the wonderful equations,

equations 19 and 20:

⊙

= 107.52 ≈ 108

moon

= 110 ≈ 108

⊙

6.957E8m

6,371,000m

= 109 ≈ 108

K E

= n

⊙

⋅

2ℏ

⊙

planet

moon

≈

star

moon

⊙

6.96E8m

1737400m

= 400.5986

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19.

20.

unify the Mesopotamian system with the Hindu system because

This suggests that the Hindu system is just as Natural as the Western system.

Ancient Aliens

How could have The Ancient Mesopotamians known

And, the Ancient Hindus have known

earth

ℏ

⊙

7.05E 33

2.8314E 33

= 2.4899 ≈ 2.5 = 2

earth

ℏ

⊙

24 = 60

1vi spal a = 0.4 secon ds

(0.4s)(2.5) = 1secon d

(

6α

4πh

)

⋅

= 1secon d

(

(Ear th Da y)

)

⋅

⊙

= 1secon d

⋅

π r

G m

⋅

= 1secon d

moon

ℏ

⊙

(2.8314E 33)

(6.67408E − 11)(7.34763E 22kg)

= 3.0281E8m

moon

3.0281E8m

299,792,458m /s

= 1.010secon d s

moon

= 1secon d

⊙

= 107.52 ≈ 108

moon

= 110 ≈ 108

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It lends one to suggesting the influence of Ancient Aliens. I may have found traces of it. Let us go

into that story now.

Abstract

After developing a a single theory for atomic systems and planetary systems, I have found that

the unit of a second for measuring time, which ultimately came to us from the Ancient

Sumerians, who ﬁrst settled down from following the herds and hunting with stone spearpoint to

invent writing, mathematics, agriculture and metallurgy along the Tigris and Euphrates rivers of

Mesopotamia, is a Natural constant.

There has been some suggestion by many scholars that, since this invention of civilization by

the Sumerians happened mysteriously almost overnight on an archaeological time scale, that

they were given knowledge by Ancient Aliens. The Sumerians themselves said in their writings

in their ancient cuneiform that the they were given their knowledge from “Those who came from

the heavens”.

I am able to suggest that traces of such Aliens may exist in ancient records and contemporary

UFO sightings, and that the two are connected. I show this connection may be rooted in the

idea of the unit of a second for measuring time as a Natural constant, that it is a basis unit for

describing atomic systems, planetary systems, and biological systems in common.

⊙

6.957E8m

6,371,000m

= 109 ≈ 108

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Introduction !

I developed a theory that solves both the atom and the solar system in terms of a base unit of

1 second and quantization of the system with the Earth’s moon. When working out the theory

the base unit of time came out to be 1 second, and I thought that was rather incredible

because the second came to us ultimately from the Ancient Sumerians who mysteriously

settled down from hunting with stone spearpoint and inventing agriculture, mathematics, and

astronomy, but we would hazard to guess they didn’t know about a wave equation solution for

the solar system or the radius and mass of the atom’s proton, let alone of the proton itself, that

all came much later with modern science.!

What was even more compelling was that this unit of a second occurred in many forms in

terms of many diﬀerent things in the theory. I found:!

Where is the kinetic energy of the Moon, is the kinetic energy of the Earth, is the

ﬁne structure constant is 1/137, is the rotation period of the Earth 24 hours, is

Planck’s constant, is the universal constant of gravitation, is the speed of light, is the

radius of the proton, is the mass of a proton, is a wavelength associated with the

Moon in the theory, is the mass of the Moon, is the mass of the Earth, is the mass

of the Sun, is the diameter of the Earth’s orbit, is the orbital velocity of the Moon, and

is the orbital velocity of the Earth, 3 is the Earth orbital number.!

In part 1 we already went into how I arrived at all that. I would like to go into the theory that we

may have ultimately got our unit of a second for measuring time from ancient aliens who may

have given it to the Ancient Sumerians who started civilization, the Ancient Sumerians from

whom we got writing, mathematics, and agriculture.!

1secon d =

(Ear th Day)

(

6α

4πh

)

⋅

= 1secon d

⋅

πr

⋅

= 1secon d

moon

= 1secon d

1secon d = d

⊙

Ear th Day

moon

⊙

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We have the unit of a second today because the Ancient Sumerians had a base 60 system of

counting (sexagesimal it is called). The Sumerians divided the day into 12 hours, evenly

divisible into 60, and so from sunrise to sunrise was 24 hours, and from sunset to sunset was

24 hours. They multiplied 60 by 6, to get 360 degrees in a circle. Since the Earth does one orbit

around the Sun in 365 days, which is a year, the Earth goes through about 1 degree a day. The

Babylonians got that from them, and further divided the hour into 60 minutes, and the minute

into 60 seconds, though hours were in their sun dials, they only used minutes and seconds for

astronomy. The West, the Europeans, got their sun dials from the Babylonians but did not

incorporate minutes and seconds into their mechanical clocks until the 17th century, but it all

came from the Sumerians, who settled down from hunting with stone spearpoint and started

agriculture, writing, mathematics, and civilization in general. Sun dials were used in Egypt as

well and had 12 divisions throughout the day as well for hours. A sun dial simply tells time by

the angle of a shadow cast by the Sun as the sun rises and sets, its position measuring time.!

The interesting thing is that we have the duration of a second is what it is not because we were

attempting to find some base unit of time for Nature, but rather we have the duration of a

second from ancient times that came to us over many years of dividing the rotation of the Earth

into hours, minutes, and seconds in such a way that we ended up with it. However we may have

had some sort of a thought going into it that was six-fold in Nature that lead it to being natural if

we consider:

And that thought may be was in a six-fold pattern that the motions of the Earth/Moon/Sun

system had in it approximately which we inadvertently characterized in the calendar:

Which can be written

Where there are 360 degrees in a circle and as such the Earth approximately moves through one

degree per day around the Sun. We achieved this because the ancients of Sumeria and Babylonia

from which the ancient Greeks received their counting system used base 60, sexagesimal

because 60 is evenly divisible by so much, that is by

1,2,3,4,5,6, 10, 12, 15, 20, 30,…

My Guess That Panned Out

I thought we might want to look for clues in present times for the possibility of aliens who may

still be coming here, in the reports of UFO’s.

I have undertaken this, and thought what a better way than to look at how we measure the

ancient second with modern clocks. The ancients did it with the position of the Sun in the sky

which comes from the rotation of the Earth, that turns once in 24 hours giving us the length of

the day, but that is not a very precise way to do it because the rotation of the Earth can waver in

1secon d =

365.25

⋅

= 0.0000000316881year

(

360days

year

)(

24h ours

d a y

)(

60mi n

h our

)(

60sec

min

)

= 31104000secon d s /year

(

60days

year

)(

1h our

d a y

)(

60mi n

h our

)(

60sec

min

)

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its period due to gravitational influences from other bodies in the solar system, like the Moon,

the Sun, and the planets.

We started with sun dials in ancient times, moved to gear ratios for clocks in medieval and

renaissance Europe, but in contemporary times we moved to oscillators, like the quartz crystal

oscillators in digital wrist watches, which is much more accurate. After that we got more

accurate with atomic clocks that make use of cesium. Quartz crystals and Cesium both occur in

Nature, and we mine them for making clocks.

In the 1980s the advent of solid-state digital electronics allowed for quartz timekeepers and

these are the mostly widely used today in most clocks and watches. If a quartz crystal is

appropriately shaped it will oscillate at a frequency of 32768 Hz, that is, 32768= oscillations

per second. Thus we began to define the second as that many oscillations of a quartz crystal.

Of course, over a year, a watch made from quartz crystals might lose a second or two over a year,

and more accurate is an atomic clock using cesium 133, the only stable isotope of cesium. The

second is now defined by 9,192,631,770 cycles of oscillations of the cesium atom.

Thus the first place I looked in hopes of finding clues to the existence of extraterrestrials,

extraterrestrials who may have given us the second in ancient times, was where cesium is found

and mined. It turns out it is a rare element and its most abundant deposits are in the province of

Manitoba in Canada, a place called Bernic Lake, in its South East corner. I then looked for UFO

sightings in Manitoba, and to my surprise found the most well documented UFO sighting in

Canada was there at Falcon Lake near the capitol Winnipeg which is right near Bernic Lake

where Cesium for clocks to define the second is primarily mined.

Interestingly, the Falcon Lake UFO sighting was in 1967 (May 20), the year we defined the

second with the cesium atomic clock, and was right near Bernic Lake where the cesium is

primarily mined. It involved a ship landing and a geologist that saw it, and approached it, Stefan

Michalak, who was hiking there looking for quartz deposits of all things, to stake a mining claim.

I thought perhaps the extraterrestrials were in the area looking for cesium, or quartz (which

occurs there as well) for their ship clocks.

To see the proximity of Falcon Lake of the UfO sighting, and Bernic Lake where Cesium is

primarily mined, to one another, and with the capitol of the province of Manitoba, go to the

maps on the next page…

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The Falcon Lake UFO Incident

Just how did the Falcon Lake UFO incident unfold? Steve Michalak was out inspecting a quartz

vein when he he saw two objects hovering 45 meters (150 ft) away from him glowing red. One

of the objects landed nearby and took on a disk shape. The other craft ﬂew off. Before

approaching the craft Steve sat and drew it for half an hour. He noticed the craft lacked any

seams and had no insignias, and looked like smooth metal. It was 10.5 meters (34 ft) in

diameter, and 4.5 meters in height (15 ft).

He noticed a door was open with light coming out, and heard voices of people talking. He

attempted to communicate with them in English to offer mechanical support, but they did not

respond and he tried in Polish, Russian, and German to no avail. He touched the craft and the

ﬁngertips of his gloves melted, it was so hot.

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The craft then rotated revealing a grid of holes that emitted a blast of heated gas that hit him in

the chest, setting his clothes a ﬁre, which he took off and the craft ﬂew away. After returning

home he sought medical attention at Misericordia Health Center for his injuries and nausia

where he was admitted to the emergency room. His injuries were conﬁrmed by the doctors, with

gridline burns on his chest and stomach. It was conﬁrmed he had radiation poisoning. He was

never convinced he saw a UFO that was alien but rather an experimental aircraft. The incident

was investigated by the Royal Canadian Mounted Police, the Royal Canadian Air Force, The

Department of Health, Department of National Defense, and American authorities the Aerial

Phenomena Research Organization and the United States Air Force as a part of the Condon

Committee. That is just a brief synopsis so I will leave the detailed story to books on the subject.

Cesium Clocks And the Ancient Constant of Nineveh

All that remains to be done now is to connect the Ancient Sumerians with modern cesium

atomic clocks that now deﬁne the unit of a second. It may seem a daunting task, but it can be

done.

The Ancient Sumerians who settled down in the Middle East (Mesopotamia) from following the

herds and hunting with stone spearpoints, to invent agriculture, mathematics, writing,

government, and metallurgy, did so almost overnight on an archaeological timescale and it has

been a mystery of archaeology just what caused this to happen.

Apparently, in their writing, cuneiform, which presses symbols into clay tablets with a stylus, the

Sumerians say they got their knowledge from “the Anunaki, those who came from above”.

According to Zecharia Sitchin, the word Nephilim in the Bible came from the Sumerians. Even

mainstream archaeology today says that the stories of the Bible had their origins in Sumerian

stories. Nephilim is Hebrew for “Those who came from above”, but it is translated as giants. I

asked a yiddish scholar why this is and he said it is because those who came from above were

giants.

Moving on, with the unearthing by archaeologists of the Assyrian civilization in current day Iraq,

and discovery of the palace and library of King Assurbanipal in Nineveh, we now had access to

some 30,000 Sumerian cuneiform tablets. Some of what was in them years later found their way

to NASA scientist, Maurice Chatelain, who oversaw the communications systems of the Apollo

missions to the Moon.

The language of Sumerian was decoded in 1846 by an Englishman, Henry Rawlinson, using

tablets with the same text inscribed in three different languages, thus breaking the code. In 1872

they were ﬁnally translated by the English Assyriologist, George Smith. Chatelain writes in his

book “Our Cosmic Ancestors”:

Among the tablets translated by Smith was a certain quantity that contained nothing but numbers,

fantastically huge numbers, apparently derived from complicated calculations…

I have not been able to ﬁnd out to this day when and where somebody decided to study these

mathematical tablets again, but the translation into our decimal system was ﬁnally published a few years

ago, and one number stood out. It consisted of ﬁfteen digits: 195,995,200,000,000…

I personally discovered the existence of the number in 1955,…

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One day I remembered that the Sumerians, who were the ancestors of the Babylonians, who were in turn

invaded by the Assyrians, used calculations based on multiples of 60 more than 3,000 years ago. We still

do not know for sure who the Sumerians were and where they came from but we have found out that they

were truly great astronomers who knew the revolution periods of all the planets of the solar system,

including Uranus and Neptune…

They were the ones who divided the day into 86,400 seconds with 24 hours of 60 minutes of 60 seconds

each. Immediately the realization came to me that the number of Nineveh represented a very, very long

long period of time expressed in seconds!…

The thought ﬂashed into my mind that the clever Sumerians were familiar, among other things

astronomical, with the precession of the equinoxes — the turning of the terrestrial axis of rotation around

the pole of the ecliptic. This movement has a cycle of 9.540 million days or about 26,000 years.

…When I divided the Nineveh number by the cycle of the precession of the equinoxes, also called The

Big Year, I had the greatest surprise of my life! The sacred number of Nineveh divided exactly into 240 Big

Years of 9.450 million days each…

Then came my conclusion that this enormous number of Nineveh could very well be the long lost magic

number called the ‘great constant of the solar system’ the number that alchemists, astrologers, and

astronomers had been looking for for a very long time, while their ancestors were familiar with it more

than 3,000 years ago…

To put it short, Chatelain tested this and found the Nineveh constant was exact multiples of the

conjunction periods of all the planets.

This constant was the number I needed to suggest that the Ancient Sumerians got the unit of a

second, which came from their sexagesimal counting system, from extraterrestrials. I suggest

extraterrestrials, because the second I ﬁnd is a base unit that describes a quantum mechanical

solution of the solar system and the atom’s proton in common, as in the equations presented at

the beginning of this paper. In other words, the second might not be arbitrary, but a natural

constant. I can suggest this because we now deﬁne the second not with dividing up the rotation

period of the Earth, but with cesium atomic clocks, which started in 1967 the year Canada’s

most famous and well documented UFO landing was sighted, and that was sighted in one of the

only reserves of the rare element cesium that makes atomic clocks possible.

Here is how we do it. The Nineveh constant is 1.959552E14 seconds/cycle. The second is now

deﬁned as 9,192,631,770 cycles of the cesium atom per second. We have

A day has 86,400 seconds:

NinevehConsta nt

CesiumOscillat ion s

1.959552E14

9,192,631,770

= 21,316.5507

sec

c ycle

21,316.55057

sec

c ycle

= 146.0018855

sec

c ycle

≈ 146

sec

c ycle

(

86,400

sec

day

)(

c ycle

146sec

)

= 591.7808

c ycle

day

≈ 592

c ycle

day

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A year is 365.25 days, but this is a cycle of the Earth around the Sun so we have:

It is the golden ratio. But we have to take the square root to get the right units. A particular

approximation we have to is found in Ancient Egypt. While the Sumerians started civilization

that spread throughout the world, the Ancient Egyptians did the same at the same time

independently, but they were isolated by ocean mountains and desert so no one invaded them,

like Semitic tribes with the Sumerians. However, they did much similar to the Sumerians, like

dividing the day into 12 hours as well. And, there has been much theorizing that Ancient Aliens

gave them a great deal, like the pyramids, whose construction cannot be explained. Questions

remain how such large, heavy stones were cut, moved, and stacked to make them.

In Maurice Chatelain’s book “Our Cosmic Ancestors” Chatelain suggests the pyramids were

landing beacons for alien craft because they were polished, and reﬂective, and were ﬂat on top.

But, I would like to point out when Chatelain solves the mathematical proportions of the

pyramids he suggests it is because the ancient Egyptians approximated the golden ratio, ,

above in our cesium clocks and the constant of Nineveh, as and the pi ( ) the ratio of the

circumference of a circle to its diameter as . In the pyramids Chatelain had to reconcile

and with one another, which don’t reconcile except in the Egyptian approximations to these

values above if we take the square root of , as we have to do above with . We

have for our cesium clocks with respect to the Nineveh constant as Chatelain suggests we have

for the pyramids:

So this all has to do with the number

So the Nineveh constant that the ancient Sumerians wrote down thousands of years ago at the

dawn of civilization not only describes the periodic motion of the planets, planets that during the

18th century at the birth of modern science we did not even know existed, which Maurice

Chatelain said divide evenly into it to four places after the decimal, not only does it do that, it

describes the oscillations of a cesium atom in its ground state that deﬁne a second, a second

that I have shown in theory is a natural constant at the basis of describing the planets and the

592

cycle

day

365.25

day

cycle

= 1.62

c ycle

day

≈ 1.618 = Φ

c ycle

day

196

121

c ycle

day

Φ ≈

196

121

= 4

Φ ≈

= 1.272727...

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atom in common. And, it does so via the relationship between the golden ratio and pi that the

Ancient Egyptians used to construct their pyramids. In turn, this cesium, which is ideal for

making such clocks was in the end used to deﬁne the second more accurately and made the

standard in 1967 when one of the most well documented UFO landings was reported in detail,

with much evidence to back it up, near Winnipeg, the capitol of the Manitoba providence where

most of the Cesium is mined for making such clocks. The Ancient Sumerians have been a

mystery to archaeology, how they settled down from hunting with stone spearpoints to invent

writing, mathematics, metallurgy, and agriculture. Also mysterious are the ancient Egyptians,

who invented mathematics, writing and agriculture around the the same time as the ancient

Sumerians independently and separately, especially their enormous stone pyramids stacked

with enormous stone blocks to precise Mathematical dimensions that we cannot even ﬁgure

today how they could have been cut, transported, and lifted. Did the ancient Sumerians and

Egyptians get their start in inventing civilization from visitors from another world more advanced

than ourselves? Can we ﬁnd indications of the presence of such visitors in ancient and

contemporary times, and are there clues that show them to be the same people?

I also found that UFOs are prominent in Canada, and are most abundant in the Manitoba

providence where the cesium is mined. In fact most of their sightings are around the capital of

Manitoba, Canada Winnipeg near the cesium mines and the Falcon Lake UFO incident. A

Manitoba news station did a story on it saying Manitoba is a UFO hotspot, with most of the

sightings in Winnipeg, significantly. They reported the numbers of sightings in cities in

Manitoba up to 2016 when the story was released. They are:

Winnipeg 767, Carman 53, Brandon 45, Thompson 40, Sperling 36

I immediately knew to look to Manitoba, Canada after I learned cesium was abundant there

because Todd, who goes by the name of “Taken by the Greys”, said on Canadian radio that he

was abducted by grey aliens at lake Manitoba, and by a secret people in Black Suits. He said he

was the one who ﬁrst said there were men in black suits, and that it is from him that they got the

idea for the ﬁlm “Men in Black”, a science ﬁction movie about men and women who wear black

suits and oversee our relationships with extraterrestrials on Earth. Todd has a Youtube channel

where he has documented his abduction at Lake Manitoba, it goes by the name of Taken by the

Greys.

I have found that the basis unit of one second is not just a Natural constant for physical systems

like the atom and the planets around the Sun, but for the basis of biological life, that it is in the

sixfold Nature of the chemical skeletons from which life is built, the hydrocarbons.

We return to a couple of the equations at the beginning of this paper…

The first can be written:

1secon d =

6α

⋅

4πh

1secon d =

K E

(Ear th Da y)

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14)

15)

From which instead of saying the left sides of these equations are seconds, we say they are

proton-seconds by not letting the units of cancel with the bodies of these equations on the

left, which are in units of mass, but rather divide into them, giving us a number of protons. I say

this is the biological because these are the hydrocarbons the backbones of biological chemistry.

We see they display sixfold symmetry. I can generate integer numbers of protons from the time

values from these equations for all of the elements with a computer program. Some results are:

A very interesting thing here is looking at the values generated by the program, the smallest

integer value 1 second produces 6 protons (carbon) and the largest integer value 6 seconds

produces one proton (hydrogen). Beyond six seconds you have fractional protons, and the rest of

the elements heavier than carbon are formed by fractional seconds. These are the hydrocarbons

the backbones of biological chemistry. And carbon is the core element of life. We see the

duration of the base unit of measuring time, 1 second, given to us by the ancients, is perfect for

the mathematical formulation of life chemistry. Here is the code for the program, it finds integer

solutions for time values, incremented by the program at the discretion of the user:

h 4π r

= 6pr oton ⋅ secon d s = carbon(C )

h 4π r

= 1pr oton ⋅ 6secon ds = hydrogen(H )

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#include <stdio.h>

#include <math.h>

int main(int argc, const char * argv[]) {

int n;

float value=0, increment,t=0, p=1.67262E-27, h=6.62607E-34,G=6.67408E-11,

c=299792458,protons[100],r=0.833E-15;

{

printf("By what value would you like to increment?: ");

scanf("%f", &increment);

printf("How many values would you like to calculate for t in equation 1 (no more than 100?): ");

scanf("%i", &n);

}

while (n>=101);

{

for (int i=0; i<n;i++)

{

protons[i]=((137*137)/(t*p))*sqrt(h*4*(3.14159)*(r*r)/(G*c));

int intpart=(int)protons[i];

float decpart=protons[i]-intpart;

t=t+increment;

if (decpart<0.25)

{ printf("%.4f protons %f seconds %f decpart \n", protons[i], t-increment, decpart);

}}}}

The Geographic Layout For UFOs and Cesium Mines

Interestingly, a straight line south from Falcon Lake where the UFO sighting was connects with

Houston, NASA’s location of mission control for space flights. I thought perhaps I was looking at

extraterrestrial navigation routes. The line of Falcon Lake to Houston, connects with Baja

Mexico, and that with Seattle, Washington a hub of tech Industry, where Microsoft is. A square

is made that encloses the United States nicely whose center is Denver, Colorado and Boulder

Colorado, Denver a so-called Beta World City, which means it is a primary node in the global

economic Network. Boulder Colorado maintains one of our Cesium atomic clocks that we use to

keep track of time accurately for science and calendars. It is a one of a handful of laboratories

that does this. See the maps and drawings below:

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The green square in the south-east corner just south-east of Winnipeg is Falcon Lake, the grey

circle just north of there (Just north-east of Winnipeg is Bernic Lake). They are very close to one

another.

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Closing Statement

We are at a time in our history when we have built telescopes that we have been able to put in

space. They have enabled us to detect some of the tiny specks orbiting other stars that are

planets, tiny specks that we always guessed should exist if our theory was right that planets

orbiting other stars are common place. Some of these planets that we have found have turned

out to be like the Earth, solid and at the right distance from their star to not be too hot for water

to vaporize, or too far for it to freeze, but for it exist in its liquid phase, a condition we believe to

be necessary for life to happen as we understand it.

We are further at a time in our development where we can leave the Earth and explore some of

the planets orbiting our star, the Sun. Our technology in the realm of computing power, as

achieved with solid state technology and integrated circuitry in our computers has taken off into

beyond what we ever dreamed it would reach so early on. It has enabled us make robotic landers

and send them to Mars to send back information about its terrain, whether it has water and can

be colonized, a necessity for us to do because resources on Earth are finite, and our survival in

the end depends on us being able to expand out into space.

But these are interplanetary missions, and in the end we need to travel between the stars. While

the planets orbiting our Sun are accessible — it takes about a year with current technology to get

to Mars — the distances between the stars are immense, with current technology it would take

thousands of years to reach the nearest one. Space is inhospitable: its is cold and devoid of air, it

is a major undertaking just to leave the Earth and go to the Moon that takes months of planning;

we can’t just press a button and take off and go there at anytime we wish.

But computers are not just making developments in the physical and biological sciences, giving

us an idea or our origins, where we going, and what we are about, they are making

advancements in our ability to engineer better ones of them, themselves; the ability to make

more complex computations quicker and store information in smaller and smaller volumes.

With such computing power we may be able to develop a way to not just travel to the planets of

our star system, but to travel to the planets of other star systems.

This I believe is important to do. Especially in light of this study. Because, through it, we see the

solar system and the atom have a profound structure mathematically that is interconnected, and

we have to ask, why our solar system has this apparent design, and the Earth has such favorable

conditions to support life over the billions of years needed for life to develop into something as

sophisticated as the human, that can alter its environment in its favor to such a degree that no

other animal has ever achieved.

We have to ask if this is not just true of our star system, but of other star systems; there are

many kinds of stars, big hot ones, and small cool ones. If our solar system in its mathematical

structure reveals so much about us, what does the mathematical structure of other star systems

reveal about the inhabitants of their planets? Are the different star systems related but different,

and if so what would that tell us about our purpose in life, or its meaning?

In order to to make the jump to the stars, we have to undergo an expansion of consciousness to

adapt to space travel and its implications. It may be we will soon find that there is already a

social structure for the different worlds in common that allows for the different space faring

civilizations to function together, and that Earth might be invited to join such an intergalactic

community. I leave this paraphrasing a poem by the astronomer Carl Sagan:

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The surface of the Earth is the shore of cosmic ocean

From it we have learned most of what we know

Some part of our being knows this is from where we came

Recently, we have waded out to sea, enough to wet our toes

Some part of our being knows this is from where we came

We long to return

These aspirations, I think, are not irreverent

Though they may trouble whatever Gods may be.

It would seem Manitoba UFO activity is happening again in the same areas as the falcon lake

incident and near the cesium mines. The following video shows compelling footage:

https://www.youtube.com/watch?v=Ykg_aNVxYAo

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Biological Life Part of a Universal Natural Process In The Universe

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Introduction I have a theory for the star systems, the planets and their suns, wherein such

systems are solved with the Schrödinger wave equation that is used to solve atomic systems. The

result is that star systems and atomic systems, systems on the macro scales and micro scales, are

governed by the same underlying principles. It came to pass that this theory indicated an

overlap with biological systems indicating that biological life could be part of the same idea, and

that is what I hope to pull out of that paper and develop here.

The theory for the planets, which also predicted the radius of a proton, which is one of the

fundamental particles out of which matter is made, suggested that star systems which support

life are a part of a Universal natural process. One of the conditions for star systems that support

life made use of the interesting fact that has mystified science for some time now, that the Moon

is the right size and distance from the Earth that it nearly perfectly eclipses the Sun. The reason

a moon would be necessary for life to be optimally successful on a habitable planet is that we

know our moon that orbits our Earth, makes life here successful because it holds the Earth at its

inclination to its orbit around the Sun allowing for the seasons, thus preventing extreme hot and

extreme cold.

Interestingly, the solution for the planets of the Schrödinger wave equation, was quantized in

terms of the Earth’s moon, and a base unit of one second. The Moon seems to be some sort of a

natural yardstick. The strange thing is that the basis unit of time is one second and the second

was not developed with the planets and atoms in mind, so it is strange that it lands upon the

function of a natural constant in our theory. In the theory (An Abstract Theory of Reality,

Beardsley 2024) I talk a little about why that might be. The second came to us from the Ancient

Sumerians, who invented civilization with settling down from following the herds and hunting

with stone spearpoint to invent agriculture, metallurgy, writing, and mathematics. They had a

base 60 counting system, and found it convenient then to divide the Earth day (rotation period)

into 24 hours, which in the end became adopted by the world. Their base 60 counting resulted in

the Babylonians dividing the hour into 60 minutes, and that in turn into 60 seconds, and that is

how we have the duration of a second we have today. They chose base 60 (sexagesimal) because

60 is evenly divisible by so much from which they gave us the 12 hour day and 12 hour night or

24 hour day from sunrise to sunrise, sunset to sunset. 12 times 5 is 60, also 60 times 6 is 360,

they gave us the 360 degree circle as well.

In this paper I show that the same unit of a second that describes planetary systems and atomic

system in common describes hydrocarbons, the skeletons of biological life chemistry. I further

show that it predicts the atomic radii of the hydrogen and carbon atoms from which such

skeletons are made. Hydrogen and carbon are the most abundant elements in life chemistry,

carbon is the core element upon which life is made, and hydrogen is the simplest element,

element one in the periodic table of the elements, consisting of 1 proton, and is the most

abundant element in the universe by far, and plays the dominant role in all of chemistry.

of 36 65

A Theory For Biological Hydrocarbons I have found that the basis unit of one second is

not just a Natural constant for physical systems like the atom and the planets around the Sun

(See my paper An Abstract Theory of Reality, Beardsley 2024) but for the basis of biological

life, that it is in the sixfold Nature of the chemical skeletons from which life is built, the

hydrocarbons. I found

1).

2).

Where is the fine structure constant, is the radius of a proton, is the mass of a

proton, is Planck’s constant, is the constant of gravitation, is the speed of light, is the

kinetic energy of the Moon, is the kinetic energy of the Earth, and is the

rotation period of the Earth is one day.

The first can be written:

3).

4).

From which instead of saying the left sides of these equations are seconds, we say they are

proton-seconds by not letting the units of cancel with the bodies of these equations on the

left, which are in units of mass, but rather divide into them, giving us a number of protons. I say

this is the biological because these are the hydrocarbons the backbones of biological chemistry.

We see they display sixfold symmetry. I can generate integer numbers of protons from the time

values from these equations for all of the elements with a computer program. Some results are:

1secon d =

6α

⋅

4πh

1secon d =

K E

(Ear th Da y)

α = 1/137

K E

Ear th Da y

h 4π r

= 6pr oton ⋅ secon d s = carbon(C )

h 4π r

= 1pr oton ⋅ 6secon ds = hydrogen(H )

of 37 65

A very interesting thing here is looking at the values generated by the program, the smallest

integer value 1 second produces 6 protons (carbon) and the largest integer value 6 seconds

produces one proton (hydrogen). Beyond six seconds you have fractional protons, and the rest of

the elements heavier than carbon are formed by fractional seconds. These are the hydrocarbons

the backbones of biological chemistry. And carbon is the core element of life. We see the

duration of the base unit of measuring time, 1 second, given to us by the ancients (the base 60,

sexagesimal, system of counting of the Sumerians who invented math and writing and started

civilization), is perfect for the mathematical formulation of life chemistry. Here is the code for

the program, it finds integer solutions for time values, incremented by the program at the

discretion of the user:

#include <stdio.h>

#include <math.h>

int main(int argc, const char * argv[]) {

int n;

float value=0, increment,t=0, p=1.67262E-27, h=6.62607E-34,G=6.67408E-11,

c=299792458,protons[100],r=0.833E-15;

{

printf("By what value would you like to increment?: ");

scanf("%f", &increment);

printf("How many values would you like to calculate for t in equation 1 (no more than 100?): ");

scanf("%i", &n);

}

while (n>=101);

{

for (int i=0; i<n;i++)

{

protons[i]=((137*137)/(t*p))*sqrt(h*4*(3.14159)*(r*r)/(G*c));

int intpart=(int)protons[i];

float decpart=protons[i]-intpart;

t=t+increment;

if (decpart<0.25)

{ printf("%.4f protons %f seconds %f decpart \n", protons[i], t-increment, decpart);

}}}}

We have that

Since this 6 seconds is also proton-seconds we have

5). is carbon (C)

6). is hydrogen (H)

⋅

4πh

G c

= 18769

0.833E − 15

1.67262E − 27

4π (6.62607E − 34)

(6.67408E − 11)(299,792458)

= 6.029978s ≈ 6s

6pr oton s

⋅

4πh

G c

= 1secon d

1pr oton

⋅

4πh

G c

= 6secon d s

of 38 65

Our Theory For Hydrocarbons With all that has been said we are equipped to proceed. We

want to consider the radius of a hydrogen atom and the radius of a carbon atom. The radius of

a carbon atom given in your periodic table of the elements is often 70 to 76 picometers. The

covalent radius of hydrogen is given as 31 picometers. The atomic radius of hydrogen is 53

picometers and the atomic radius of carbon is 67 picometers. We want to consider the atomic

radii of both, because the covalent radius, determined by x-ray diﬀraction for diatomic

hydrogen, is the size of two hydrogen atoms joined H2 divided by two, where it is measured

that way, joined, in the laboratory. Carbon is C2 divided by 2. We are interested in the single

carbon and hydrogen atoms, because we want to know what our theory for their six-fold

symmetry with one another in their representations in proton-seconds says about the way they

combine as the skeletons of life chemistry. We start with the Planck constant, which is like

ﬂux, a mass (perhaps a number of particles) per second over an area. That is it is kilograms per

second over square area:!

We have equations 1 and 2:!

1). is carbon (C)

2). is hydrogen (H)

We can write these

3).

4). !

We have from 3 and 4…!

5). !

We ﬁnd the ratio between the surface areas of the hydrogen and carbon atoms:!

h = 6.62607E − 34J ⋅ s = 6.62607E − 37

⋅ m

6pr oton s

⋅

4πh

G c

= 1secon d

1pr oton

⋅

4πh

G c

= 6secon d s

(

6.62607E − 37

⋅ m

)

6secon d s

(

6.62607E − 37

⋅ m

)

6secon ds

1.67262E − 27kg

= 2.37689E − 6m

(

6.62607E − 37

⋅ m

)

1secon d

(

6.62607E − 37

⋅ m

)

1secon d

6(1.67262E − 27kg)

= 6.602486E − 8m

⋅

(6seconds)

⋅

(1second)

2.37689E − 6m

6.602486E − 8m

= 35.9999 ≈ 40

of 39 65

6). !

7). !

It is the golden mean. These atomic radii are the radii between the nucleus of the atoms and

their valence shell, which is what we want because the valence shell is the outermost electrons

responsible for the way the hydrogen and the carbon combine to make hydrocarbons. We will

write this!

8). !

I am guessing the reason we have the golden mean here is that it is the number used for

closest packing. But what we really want to do is look at the concept of action, for hydrogen

given by six seconds and carbon given by 1 second. We take equations 1 and 2:!

1). is carbon (C)

2). is hydrogen (H)

And, we write

9).

Where is the radius of the atom, and t its time values given here by equations 1 and 2. We have for

hydrogen

10).

This is actually very close to the radius of a hydrogen which can vary around this depending on how you

are looking at it, which we said is given by 5.3E-11m. For carbon we have:

11).

And this is actually very close to the radius of a carbon atom which is 6.7E-11m. The thing is if we consider

the bond length of the simplest hydrocarbon CH4, methane, which can be thought of as

surface

= 4π (r

) = 3.52989E − 20m

surface

= 4π (r

) = 5.64104E − 20m

4π(53pm)

4π(67pm)

= 0.62575 ≈ 0.618... = ϕ

= ϕ

6pr oton s

⋅

4πh

G c

= 1secon d

1pr oton

⋅

4πh

G c

= 6secon d s

G c

∫

dt = r

G c

∫

dt = (1.67262E − 27kg)

(6.67408E − 11)(299,792,458)

6.62607E − 34

∫

6sec

(9.2E − 12m /s)(6secon d s) = 5.5E − 11m

G c

∫

dt = (1.67262E − 27kg)

(6.67408E − 11)(299,792,458)

6.62607E − 34

∫

6sec+1sec

(9.2E − 12m /s)(7secon d s) = 6.44E − 11m

of 40 65

16).

our, equations give

17).

which are the same thing. Thus we have the basis for a theory of everything in that it includes the macro

scale, the Earth/Moon/Sun System, because we had:

and it includes the radius of the proton which is the radius and mass of a proton and gives 1

second

and we have the hydrocarbons the skeleton of the chemistry of life give one second

1). is carbon (C)

2). is hydrogen (H)

and because they predict the radii of the carbon and hydrogen atoms at the core of life

10).

11).

+ r

= 5.3E − 11m + 6.7E − 11m = 1.2E − 11m

+ r

= 5.5E − 11m + 6.44E − 11m = 1.2E − 11m

1secon d =

K E

(Ear th Da y)

1secon d =

6α

⋅

4πh

6pr oton s

⋅

4πh

G c

= 1secon d

1pr oton

⋅

4πh

G c

= 6secon d s

G c

∫

dt = (1.67262E − 27kg)

(6.67408E − 11)(299,792,458)

6.62607E − 34

∫

6sec

(9.2E − 12m /s)(6secon d s) = 5.5E − 11m

G c

∫

dt = (1.67262E − 27kg)

(6.67408E − 11)(299,792,458)

6.62607E − 34

∫

6sec+1sec

(9.2E − 12m /s)(7secon d s) = 6.44E − 11m

of 41 65

The Solar Formulation For The Solution Of The Wave Equation

of 42 65

The Solar Formulation

Our solution of the wave equation for the planets gives the kinetic energy of the Earth from the

mass of the Moon orbiting the Earth, but you could formulate based on the Earth orbiting the

Sun. In our lunar formulation we had:

We remember the Moon perfectly eclipses the Sun which is to say

Thus equation 1 becomes

The kinetic energy of the Earth is

Putting this in equation 3 gives the mass of the Sun:

We recognize that the orbital velocity of the Moon is

So equation 5 becomes

This gives the mass of the Moon is

Putting this in equation 1 yields

K E

= 3

⊙

⋅

2ℏ

⊙

K E

= 3

⋅

2ℏ

⊙

K E

⋅

⊙

= 3r

⋅

ℏ

⊙

= 3r

⋅ v

⋅

ℏ

⊙

ℏ

⊙

K E

⊙

⋅

⊙

of 43 65

We now multiply through by and we have

10.

Thus the Planck constant for the Sun, , in this the case the star is the Sun, is angular

momentum quantized, the angular momentum we will call , the subscript for Planck. We

have

We write for the solution of the Earth/Sun system:

11.

Let us compare this to that of an atom:

12.

We notice that in equation 11

; ; ; ;

is really . We can write 11 as

13.

We say. . That is

Let us see how accurate our equation is:

K E

⊙

⋅

⊙

ℏ

⊙

= r

= (1.496E11m)(1022m /s)(5.972E 24kg) = 9.13E 38kg ⋅

= r

= 7.4483E 77J ⋅ m

⋅ kg = 8.3367E 77kg

⋅

K E

⊙

⋅

⊙

E = −

⋅

2ℏ

→

⊙

→ G

→ M

⊙

ℏ

→ L

ℏ

⊙

K E

⊙

⋅

⊙

2ℏ

⊙

ℏ

⊙

= ℏ

⊙

/2π

ℏ

⊙

= 9.13E 38J ⋅ s

⊙

= 2π ℏ

⊙

= 5.7365E 39J ⋅ s

K E

⊙

⋅

⊙

2ℏ

⊙

of 44 65

We have that the kinetic energy of the Earth is

Our equation has an accuracy of

Which is very good.

We call the same in our solar solution. But we now want our solution for the solar

formulation. is the mass of the Earth and is the mass of the Sun. We have our solution

might be!

14. !

Where is !

We have

15.

This has an accuracy of

Thus the solutions to the wave equation!

⊙

(6.67408E − 11)

(5.972E 24kg)

(1.9891E 30kg)

2(8.3367E 77kg

⋅

)

⊙

(6.759E 30J )

⊙

6.957E8m

1737400m

= 400.426

K E

= 2.70655E 33J

K E

earth

(5.972E 24kg)(30,290m /s)

= 2.7396E 33J

2.70655E 33J

2.7396E 33J

= 98.79 %

ℏ

⊙

ℏ

⊙

⋅

⊙

ℏ

⊙

= 9.13E 38J ⋅ s

(9.13E 38)

(6.67408E − 11)(5.972E 24kg)

⋅

400.5986

= 1.4638E11m

1.4638E11m

1.496E11m

100 = 97.85 %

of 45 65

for the solar formulations are!

13)

14)

Equating The Lunar And Solar Formulations Yield Our 1 Second Base Unit

Let us equate equation 1 with equation 13:

13.

This gives:

16.

We remember that

−

ℏ

[

∂

∂r

(

∂

∂r

)

sinθ

∂

∂θ

(

sinθ

∂

∂θ

)

sin

∂

∂ϕ

]

ψ + V(r )ψ = E ψ

K E

⊙

⋅

⊙

2ℏ

⊙

ℏ

⊙

⋅

⊙

ℏ

⊙

= 9.13E 38J ⋅ s

⊙

= 2π ℏ

⊙

= 5.7365E 39J ⋅ s

K E

= n

⊙

⋅

2ℏ

⊙

K E

⊙

⋅

⊙

2ℏ

⊙

⋅

2ℏ

⊙

⋅

⊙

⋅ ℏ

⊙

ℏ

⊙

= (hC )K E

hC = 1secon d

C =

⋅

2π r

G m

of 46 65

This gives

17.

We have

18.

This equates the orbital velocity of the Moon with the centripetal acceleration of the Earth in

terms of one second by way of the mass of the Earth, the mass of the Sun, the mass of the Moon,

and the orbital number of the Earth. Let us compute

19.

Let us see how well equation 18 works. at aphelion is 966 m/s and .

. We have

That is an accuracy of

Equation 18 can be written:

20.

From our equation:

6α

h 4π r

= 1.004996352secon ds

6α

⋅

h 4π

⋅

⊙

(1secon d )

⊙

(5.972E 24kg)

(1.9891E 30kg)

(7.34763E 22kg)

(1.732)

= 321,331.459 ≈ 321,331

= 29,800m /s

= 1AU = 1.496E11m

2(966m /s) =

(29,800m /s)

1.496E11m

(1sec)(321,331.459)

1,907m /s = 1,932m /s

1907

1932

= 98.7 %

1secon d = 2r

⊙

6α

h 4π r

= 1.004996352secon ds

of 47 65

We have

21.

Since , the diameter of the Earth orbit, we have

22.

And we see the Earth/Moon/Sun system determines the radius and mass of the proton and vice

versa. We basically have

23. 62)

Where is the Earth orbital number. We have

= 7.83436E4seconds

EarthDay=(24)(60)(60)=86400 seconds,

accuracy

This last equation, equation 62, we can use to find the rotation period, or the length of the day,

of an earth-like planet in the habitable zone of any star system, so it would be very useful.

We want to turn our attention to equation 20 and write it

6α

⋅

h 4π

= 2r

⋅

⊙

= d

6α

⋅

h 4π

= d

⋅

⊙

1secon d = 2v

⊙

1secon d =

K E

moon

K E

earth

Ear th Da y

1secon d =

Ear th Da y

Ear th Da y =

⊙

n = 3

Ear th Da y =

2(1.496E11m)

966m /s

7.34763E 22kg

1.9891E 30kg

1.732

7.834E4s

86,400s

100 = 90.675 %

of 48 65

24.

We see equating solar and lunar formulations for energy yield the base unit of one second.

Equating the lunar and solar solutions for orbitals instead of the for energies, which we just did,

we have

Yields

25.

Where . The accuracy of this is

Thus the energy equations gave the equation 55:

16. !

And equating the orbital equations gives

26.

These last two yield

27.

The accuracy is

1secon d = d

⊙

2ℏ

⊙

⋅

⊙

⋅

⊙

ℏ

⊙

3/2 = cos(π /6)

(2.8314E 33)

(5.972E 24)

(7.34763E 22)

= (0.866)(9.13E 38)

(1737400)

(6.96E8)

4.29059E 72 = 4.5005E 72

4.29059E 72

4.5005E 72

100 = 95.3 %

⊙

⋅ ℏ

⊙

2 3

⋅

⊙

⋅ ℏ

⊙

= 1

of 49 65

Is 98% accuracy. The important thing that comes out of this is our base unit of a second because

we see it is also a function lunar, solar, and earth masses.

24.

(400.5986)

5.972E 24kg

1.9891E 30kg

= 1

0.98 = 1

1secon d = d

⊙

of 50 65

Wave Solutions For Jupiter And Saturn

of 51 65

Solutions For Jupiter And Saturn

We have the solution for the Bohr hydrogen atom is

is the atomic number, the number of protons orbited, but for our system it is 1, because one

body is orbited. is the orbit number, which we will deal with later. We have our solution for the

Earth/Moon/Sun system is

Let is the earth mass, is the lunar mass, and is our

Planck constant for the Earth/Moon/Sun system. We compute equation 2:

The kinetic energy of the Earth is

This is

The Moon perfectly eclipses the Sun which means as seen from the Earth the Moon appears to

be the same size as the Sun. This is because

Where is the Earth orbital distance, is the Moon’s orbital distance, is the Sun’s radius,

and is the Moon’s radius. This is because though the Moon is 400 times further from the Sun

than it is from the Earth, the Sun is 400 times larger than the Moon. That is

Thus

We find the quantum mechanical solution to the Earth/Moon/System is

E = −

)

2ℏ

E =

⊙

M = M

m = M

⊙

= 2.8314E 33J ⋅ s

E =

(6.67408E − 11)

(5.972E 24kg)

(7.347673E 22kg)

2(2.8314E 33)

3.93E 30Joules

K E

(5.972E 24kg)(30,290m /s)

= 2.7396E 33J

1/n

= 697

≈

⊙

6.96E8m

1737400m

= 400.5986

⊙

= 400

of 52 65

5 !

for Earth orbit (Third Planet).!

We see the solar Planck constant we developed works in solving the Schrödinger wave equation

for the Earth/Moon/Sun system. My belief as to why this was never done is that it had to be

realized that the solution of the Earth kinetic energy around the Sun as a quantum mechanical

state is based on the Moon around the Earth.

Now we want to find what the wave equation solutions are for Jupiter and Saturn because they

significantly carry the majority of the mass of the solar system and thus should embody most

clearly the dynamics of the wave solution to the Solar System.

I find that as we cross the asteroid belt leaving behind the terrestrial planets, which are solid,

and go to the gas giants and ice giants, the atomic number is no longer squared and the square

root of the the orbital number moves from the numerator to the denominator. I believe this is

because the solar system here should be modeled in two parts, just as it is in theories of solar

system formation because there is a force other than just gravity of the Sun at work, which is the

radiation pressure of the Sun, which is what separates it into two parts, the terrestrial planets on

this side of the asteroid belt and the giants on the other side of the asteroid belt. The effect the

radiation pressure has is to blow the lighter elements out beyond the asteroid belt when the

solar system forms, which are gases such as hydrogen and helium, while the heavier elements

are too heavy to be blown out from the inside of the asteroid belt, allowing for the formation of

the terrestrial planets Venus, Earth, and Mars. The result is that our equation has the atomic

number of the heavier metals such as calcium for the Earth, while the equation for the giants has

the atomic numbers of the gasses. We write for these planets

So, for Jupiter we have (And again using the maximum orbital velocity which is at perihelion):

E = n

⊙

⋅

⊙

n = 3

3(400.5986)(3.93E 30J ) = 2.7268585E 33J

2.7268585E33

2.7396E33

= 99.5 %

E =

2ℏ

⊙

K E

(1.89813E 27kg)(13720m /s)

= 1.7865E 35J

E =

(6.67408E − 11)

(1.89813E 27kg)

(7.347673E 22kg)

2(2.8314E 33)

E =

(3.971E 35J ) = Z

(1.776E 35J )

of 53 65

Jupiter is mostly composed of hydrogen gas, and secondly helium gas, so it is appropriate that

Our equation for Jupiter is

Where is the atomic number of hydrogen which is 1 proton, and for the orbital

number of Jupiter, . Now we move on to Saturn…

The equation for Saturn is then

It makes sense that Saturn would use Helium in the equation because Saturn is the next planet

after Jupiter and Jupiter uses hydrogen, and helium is the next element after hydrogen. As well,

just like Jupiter, Saturn is primarily composed of hydrogen and helium gas.

Our equation in this paper for the Earth orbit does not depend on the Moon’s distance from the

Earth, only its mass. The Moon slows the Earth rotation and this in turn expands the Moon’s

orbit, so it is getting larger, the Earth loses energy to the Moon. The Earth day gets longer by

0.0067 hours per million years, and the Moon’s orbit gets 3.78 cm larger per year. It is believed

the Moon came from a chunk knocked off the Earth from a collision with a Mars sized

protoplanet. At the time that the Moon formed it was about 4 Earth radii distant 4.5 billion

years ago. After 100 million years the Moon became tidally locked making its rotation period

equal to its orbital period keeping one face always towards the Earth. After 500 million years the

Moon was orbiting at about 20 Earth radii. It is believed that during the period of heavy

bombardment in a chaotic early solar system about 4.1 to 3.8 billion years ago a large object did

a close pass pulling the Moon further changing its orbit giving it its 5 degree offset from the

Earth’s equator. Our wave equation solution may only use the Moon’s mass but the equation for

1.7865E 35J

1.776E 35J

= 1.006pr oton s ≈ 1.0pr oton s = hydr ogen(H )

Z = Z

E =

2ℏ

⊙

n = 5

K E

(5.683E 26kg)(10140m /s)

= 2.92E34J

E =

(6.67408E − 11)

(5.683E 26kg)

(7.347673E 22)

2(2.8314E 33)

2.45

(3.5588E 34J ) = Z(1.45259E 34J )

Z(1.45259E 34J ) = (2.92E 34J )

Z = 2 proton s = Heliu m(He)

E =

2ℏ

⊙

of 54 65

kinetic energy of the Moon to kinetic energy of the Earth times the Earth Day equal to about one

second:

Which we connect with the equation where the proton gives one second

This holds for when the Moon was at a distance from the Earth such that it appears the same

size as the Sun, which means:

Which is when the two equations above for one second connect to our wave equation solution to

the Earth

Because .

The Moon at its inclination to the Earth in its orbit makes life possible here because it holds the

Earth at its tilt to its orbit around the Sun allowing for the seasons so the Earth doesn’t get too

extremely hot or too extremely cold. We see the Moon may be there for a reason.

K E

moon

K E

earth

(Ear th Da y) = 1.08secon ds

6α

h 4π r

= 1.004996354secon ds

planet

moon

≈

star

moon

K E

= n

⊙

⋅

2ℏ

⊙

star

moon

⊙

of 55 65

Modeling Habitable Star Systems

of 56 65

Modeling Habitable Star Systems

We want to solve a habitable planetary system in general and apply it to another star system. We

must include the solution of its moon as well, because the Moon of the Earth makes life

optimally possible. However, our Moon is counter-intuitive, it breaks all of the rules of the other

moons in our solar system. One is it has a low mass for its size. It has been said that it could be

hollow. Even suggested that it is a hollow-spacecraft put there to make life as we know it

possible. In our quantum theory for the solar system, we may have discovered the science of the

engineers who may have made the Moon, and we are possibly applying their science here. Our

quantum theory for the solar system also has a solar solution as compared to a lunar solution, so

it works for star systems in general.

The perfect star system to use for our purposes here would be Tau Ceti. Tau Ceti is a star

spectrally similar to the Sun and the closest of such a G-class star, at about 12 light years distant.

Its mass is 78% of the Sun’s. Its mass is

Its radius is:

And its luminosity is

It has several unconfirmed planets with one potentially in the habitable zone. It has been the

subject of science fiction literature. It is in the constellation Cetus. From Tau Ceti the Earth

would be seen to be in the northern hemisphere constellation Bootes with an apparent

magnitude of 2.6. It is spectral class G8 V where our Sun is G2 V.

For the luminosity of a main sequence star we only need to know the mass of the star to get its

luminosity:

This holds in solar masses and solar luminosities. The habitable zone of a star is given by

luminosity. If the star is 100 times brighter than our Sun, then the habitable zone is 10 times

further than the Earth is from the Sun by the inverse square law.

In astronomical units and solar luminosities. From we can get the orbital period in Earth

years:

We can get the radius of the Moon of the planet if we know the mass of the planet, :

= 0.783 + / − 0.012M

⊙

= 0.793 + / − 0.004R

⊙

= 0.488 + / − 0.0010L

⊙

L = M

3.5

= L

= r

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We want the mass of the Earth from the mass of the Sun. We would guess we can get it from the

mass of the Sun, the size of the Sun, and the base 60 sexagesimal system upon which we have

found everything is based. I find the relationship exists for the Earth:

(36)(5)=180=360/2 and 360/6=60 is base 60 sexagesimal. This gives

This is an accuracy of

We can get the orbital distance of the planet’s Moon from the planet:

Once we have that we can get the radius of the Moon of the planet

Now we can get the rotation period of the planet, its length of day:

Because the orbital velocity of the planet’s Moon is

We can use the the delocalization time get the moon’s mass, which is 1/2 the planet’s year, with

10 , See Appendix 1

⊙

= 1

⊙

= 0.13889(1.9891E 30kg)

6.96E8m

1.496E11m

= 5.979748E 24kg

5.972E 24

5.979748E 24

100 = 99.87 %

planet

moon

≈

star

moon

⊙

= 1

Ear th Da y =

⊙

τ =

moon

(2r

moon

)

ℏ

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And the whole system is solved. Let us see how the theoretical luminosity appears with that

measured with equation 8.1:

It is close to the measured. The equation for predicting is approximate as the actual

values can vary a little with things like metallicity of the stars. Tau Ceti has low metallicity

compared to our Sun.

Let’s find the orbital distance of the habitable planet if it exists with equation 2:

Let’s find the orbital period of the habitable planet (It’s year) with equation 3:

Let’s get the mass of the habitable planet from equation 5:

Which is good because the planet, if it exists, is thought to be larger than the Earth. Let’s get the

radius of its moon from equation 4:

Let’s see at what distance it orbits the planet with equation 6:

= M

3.5

= 0.783

3.5

= 0.425L

⊙

0.448L

⊙

= 0.488 = 0.69857AU = (0.6986AU )(1.496E11m /AU ) = 1.045E11m eters

= r

= (0.69867AU )

= 0.584years(365.25d a ys)((24hrs)(60min)(60sec) = 1849638secon d s

(0.584)(365.25d a ys) = 213.306d a ys

= (0.783)(1.9891E 30kg) = 1.5575E 30kg

= (0.793)(6.96E8m) = 5.52 E 8m

(1.5575E 30kg)

(5.52E8m)

(1.045E11m)

= 6.036E 24kg

6.036E 24

5.972E 24

= 1.0107Ear th Ma sses

= 2R

2(5.52E8m)

(6.036E 24kg)

(1.5575E 30kg)

= 1.53656E6m =

1.53656E6m

1.7374E6m

= 0.8844Lun arRa dii

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Let’s get the orbital velocity of this moon with equation 9:

So the orbital period of the moon is:

Compared to that of the Earth which is 27.3 days for the sidereal month and is a 29.53day lunar

month. The Moon of Tau Ceti would have a slightly longer lunar month, too. Now we can

determine the rotation period of the planet which would be its day:

We get the mass of the moon from equation 10:

So the rotation period of the planet (Its Day) is from equation 8:

If the moon of Tau Ceti is to perfectly eclipse its star, like our Moon does with the Sun, to let its

inhabitants know that they are there for reason, and so as to theoretically be a condition for

optimizing life, then we have the following should hold:

moon

= r

planet

moon

star

= (1.045E11m)

1.53656E6m

5.52E8m

= 2.91E8m

2.91E8m

3.84E8m

= 0.7578L un arOrbital Ra dii

(6.67408E − 11)(6.0636E 24kg

2.91E8m

= 1,176.6m /s

2π r

2π (.91E8m)

1,176.6m /s

= 1.554E6secon d s

(1.554E6s)

min

60sec

h our

60mi n

d a y

24h ours

= 17.987d a ys

ℏ

(2.8314E 33J ⋅ s)(0.5)(18429638s)

4(2.91E 8m)

= 7.7E 22kg

7.7E 22kg

7.34763E 22kg

= 1.048Ear th Moon s

Pl a n et Da y =

2(1.045E11m)

1,176.6m /s

7.7E 22kg

1.5575E 30kg

= 39495.61secon d s = 658.26min = 10.971h ours

10.971

24h ours

= 0.457Ear th Da ys

planet

moon

≈

star

moon

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We have

And it does hold. For the Earth/Moon/Sun system we get

For the Tau Ceti system the 359 is close to 360, which is a convenient amount of degrees into

which divide a circle, like we did. We see the Tau Cetians might do the same, because like us

they might choose the base 60 sexagesimal system of counting, and this 360 might influence the

way the inhabitants of a planet orbiting this star would make their calendar. Just like the 365

day year here on Earth corresponds closely to the 360 degrees of a circle. Aside from having here

on Earth the degree, we have gradians, of which there are 400 in a circle. They make it very easy

for computing right angles to a given angle. They are used more in Europe and in surveying and

architecture, though it might have some interesting connection with our 400=400.

The habitable planet of Tau Ceti would orbit it star with a period of 213 days, which would be its

year. It star is about 78% the mass of our Sun, and about 79% its size. Its habitable planet would

be a little larger than the Earth, but not much. Its Moon would be about 88% the size of our

moon, but a little bit more massive, but not much more massive. It would orbit Tau Ceti once

about every 18 days meaning there would be 11.833 months in the Tau Ceti Year, or about 12

months like we have. It would orbit the planet at about three quarters the distance ours does.

The day from sunrise to sunrise, or sunset to sunset would be about 11 hours, or close to half the

length of our day. This is if Tau Ceti was engineered for life, but it doesn’t have to have a planet

so optimally designed for life as ours. Our 24 hour day would be better for when entering the

realm of doing astronomy, because longer nights mean more complete observations of the

universe surrounding us than for the Tau Cetians. It may mean for the conditions for life to be

optimal, like here on Earth, the star would have to be as massive as the Sun, to provide a longer

year and a longer day. But we see here how the science of engineering planetary systems optimal

for life, might be done.

1.045E11m

2.91E8m

5.52E8m

1.53656E6m

359 = 359

400 = 400

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Appendix 1

If we want to prove that our planetary Planck constant is correct, the delocalization time for the

Earth should be 6 months using it, the time for the Earth to travel the width of its orbit. We want

to solve the Schrödinger wave equation for a wave packet and use the most basic thing we can

which is a Gaussian distribution. We want to then substitute for Planck’s constant that is used

for quanta and atoms our Planck-type constant (h bar solar) for the Earth/Moon/Sun system

then apply it to predict the delocalization time for the Moon in its orbit with the Earth around

the Sun.

We consider a Gaussian wave-packet at t=0:

We say that is the delocalization length and decompose the wave packet with a Fourier

transform:

is the harmonics of the wave function. We use the identity that gives the integral of a

quadratic:

Solve the equation

With the initial condition

A plane wave is the solution:

Where,

The wave-packet evolves with time as

Calculate the Gaussian integral of

ℏ

⊙

ψ (x,0) = Ae

−

ψ (x,0) = Ae

−

∫

2π ℏ

ℏ

∫

∞

−∞

−α

x+βx

d x =

4α

iℏ∂

ψ (x, t) =



ψ (x, t)

ψ (x,0) =

∫

dp ⋅ e

2ℏ

⋅ e

−

ℏ

( px−ϵ ( p)t)

ϵ( p) =

ψ (x, t) =

∫

dp ⋅ e

2ℏ

⋅ e

−

ℏ

( px−

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and

The solution is:

where

is the delocalization distance, which for instance could be the width of an atom. is the

delocalization time, the average time for say an electron to traverse the diameter of the atom and

even leave it, to delocalize. If we substitute for our , and say that the delocalization distance

is for the Moon, the width of the Earth orbit, we should get a half a year for the delocalization

time, the time for the Moon and Earth to traverse the diameter of their orbit around the Sun. We

have

Where is the mass of the Moon, and is the orbital radius of the Moon. We have

Now let’s compute a half a year…

(1/2)(365.25)(24)(60)(60)=15778800 seconds

So we see our delocalization time is very close to the half year over which the Earth and Moon

travel from one position to the opposite side of the Sun. The closeness is

Thus we know our is accurate, it continues to function in a theoretical framework. The thing

about this is that it means we can predict the mass of the Moon from the Earth year. In terms of

what we said earlier that the Moon allows for life by creating the seasons, holding the Earth at

its tilt to the Sun, so we don’t go through extreme heat and cold, this suggests the Moon has a

mass that follows from Earth orbit, which is the habitable zone of the Sun, the right distance for

water to exist as liquid, and thus could be as it is for a reason, which means life might be part of

a physical process throughout the Universe, that it unfolds naturally in the evolution of star

systems.

2ℏ

2mℏ

β =

i x

ℏ

= ex p

[

−

⋅

1 + t

/τ

]

τ =

m d

ℏ

⊙

τ =

moon

(2r

moon

)

ℏ

⊙

moon

τ = 4

(7.34767E 22kg)(3.844E8m)

2.8314E 33J ⋅ s

= 15338227secon d s

15338227

15778800

100 = 97.2 %

ℏ

⊙

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Appendix 2: The Data For Verifying The Equations

(Proton Mass)

(Planck Constant)

(Proton Radius)

(Gravitational Constant)

(light speed)

(Fine Structure Constant)

Earth day=(24)(60)(60)=86,400 seconds. Using the Moon’s orbital velocity at aphelion, and

Earth’s orbital velocity at perihelion we have:

: 1.67262 × 10

−27

h : 6.62607 × 10

−34

J ⋅ s

: 0.833 × 10

−15

G: 6.67408 × 10

−11

c : 299,792,458m /s

α : 1/137

= q

= 1.6022E − 19coulom bs

= 8.988E 9

K E

moon

(7.347673E 22kg)(966m /s)

= 3.428E 28J

K E

earth

(5.972E 24kg)(30,290m /s)

= 2.7396E 33J

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The Author!

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